Uncovering the design principles of circadian clocks: mathematical analysis of flexibility and evolutionary goals.

[1]  Albert Goldbeter,et al.  A model for the enhancement of fitness in cyanobacteria based on resonance of a circadian oscillator with the external light-dark cycle. , 2002, Journal of theoretical biology.

[2]  Yi Liu,et al.  Alternative Initiation of Translation and Time-Specific Phosphorylation Yield Multiple Forms of the Essential Clock Protein FREQUENCY , 1997, Cell.

[3]  B. Zheng,et al.  mPer1 and mPer2 Are Essential for Normal Resetting of the Circadian Clock , 2001, Journal of biological rhythms.

[4]  R. Foster,et al.  Entrainment of Circadian Programs , 2003, Chronobiology international.

[5]  S. A. Robertson,et al.  NONLINEAR OSCILLATIONS, DYNAMICAL SYSTEMS, AND BIFURCATIONS OF VECTOR FIELDS (Applied Mathematical Sciences, 42) , 1984 .

[6]  S. Kay,et al.  Time zones: a comparative genetics of circadian clocks , 2001, Nature Reviews Genetics.

[7]  Y Yang,et al.  Interlocked feedback loops contribute to the robustness of the Neurospora circadian clock , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[8]  P. Hardin,et al.  Interlocked feedback loops within the Drosophila circadian oscillator. , 1999, Science.

[9]  A. Goldbeter,et al.  Toward a detailed computational model for the mammalian circadian clock , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[10]  H. Kitano,et al.  Robust oscillations within the interlocked feedback model of Drosophila circadian rhythm. , 2001, Journal of theoretical biology.

[11]  Herschel Rabitz,et al.  The Green’s function method of sensitivity analysis in chemical kinetics , 1978 .

[12]  N. G. Parke,et al.  Ordinary Differential Equations. , 1958 .

[13]  A. Goldbeter,et al.  Chaos and birhythmicity in a model for circadian oscillations of the PER and TIM proteins in drosophila , 1999, Journal of theoretical biology.

[14]  Michael W. Young,et al.  vrille, Pdp1, and dClock Form a Second Feedback Loop in the Drosophila Circadian Clock , 2003, Cell.

[15]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[16]  J. Tyson,et al.  A simple model of circadian rhythms based on dimerization and proteolysis of PER and TIM. , 1999, Biophysical journal.

[17]  A. B. Reddy,et al.  Differential Resynchronisation of Circadian Clock Gene Expression within the Suprachiasmatic Nuclei of Mice Subjected to Experimental Jet Lag , 2002, The Journal of Neuroscience.

[18]  A. Winfree The geometry of biological time , 1991 .

[19]  D. A. Baxter,et al.  Modeling Circadian Oscillations with Interlocking Positive and Negative Feedback Loops , 2001, The Journal of Neuroscience.

[20]  A. Yasui,et al.  Disruption of mCry2 restores circadian rhythmicity in mPer2 mutant mice. , 2002, Genes & development.

[21]  A. Goldbeter,et al.  Limit Cycle Models for Circadian Rhythms Based on Transcriptional Regulation in Drosophila and Neurospora , 1999, Journal of biological rhythms.

[22]  Gregor Eichele,et al.  Nonredundant Roles of the mPer1 and mPer2 Genes in the Mammalian Circadian Clock , 2001, Cell.

[23]  A. Hall,et al.  Response regulator homologues have complementary, light-dependent functions in the Arabidopsis circadian clock , 2003, Planta.

[24]  Daniel B. Forger,et al.  A detailed predictive model of the mammalian circadian clock , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[25]  S. Daan,et al.  Assembling a Clock for All Seasons: Are There M and E Oscillators in the Genes? , 2001, Journal of biological rhythms.

[26]  M. Merrow,et al.  The Network of Time: Understanding the Molecular Circadian System , 2003, Current Biology.

[27]  J. Dunlap,et al.  Interconnected feedback loops in the Neurospora circadian system. , 2000, Science.

[28]  William H. Press,et al.  Numerical recipes in C , 2002 .

[29]  Peter Ruoff,et al.  TEMPERATURE EFFECT ON ENTRAINMENT, PHASE SHIFTING, AND AMPLITUDE OF CIRCADIAN CLOCKS AND ITS MOLECULAR BASES , 2002, Chronobiology international.

[30]  A. Goldbeter Computational approaches to cellular rhythms , 2002, Nature.

[31]  S. Kay,et al.  Orchestrated transcription of key pathways in Arabidopsis by the circadian clock. , 2000, Science.

[32]  Ueli Schibler,et al.  The Orphan Nuclear Receptor REV-ERBα Controls Circadian Transcription within the Positive Limb of the Mammalian Circadian Oscillator , 2002, Cell.